4.1.1 Effect of chemical composition on electrical resistivity
The chemical compositions of the specimens vary in Zr and Cr content, as shown in Table
I. According to Matthiessen’s law (Eq. [
1]), the electrical resistivity of an alloy is a function of the temperature-dependent electrical resistivity of the pure base metal (
ρ
pure(
T)), the specific electrical resistivity of the elements in solid solution (
ρ
i
), and their relative concentrations (
C
i
):[
18,
35]
$$ \rho = \rho_{\text{pure}} \left( T \right) + \sum\limits_{i} {\rho_{i} C_{i} } $$
(1)
In Eq. [
1], the second term represents the summation of the electrical resistivity contributions from the various solid solution elements;
ρ
i
is the specific electrical resistivity of the
ith solute and
C
i
is the concentration of this solute.
Table
IV shows the contribution of solutes in the electrical resistivity of the aluminum alloys.[
36] It can be seen that Fe and Mn have relatively greater contributions to increasing the electrical resistivity as compared to the other elements. This indicates that Fe and Mn are the primary controlling elements of the measured electrical resistivity among all the elements present in the alloy. The third effective element relative to the electrical resistivity is Zr. The increase in electrical resistivity from N1 to N3 (Figure
1) is related to the increase in the amount of Zr. By an increase in Zr content from N1 (0.08 wt pct) to N2 (0.13 wt pct) or from N2 (0.13 wt pct) to N3 (0.2 wt pct), the electrical resistivity of the alloy increases by 2 to 3 pct. In addition, N4, with a higher Cr content (0.4 pct) than the other samples, exhibits the highest electrical resistivity. The large effect of Cr on the electrical resistivity is also due to the large electrical resistivity of pure Cr compared to other elements,[
18,
35] as shown in Table
IV.
Table IV
Electrical Resistivity of Pure Alloying Elements Present in Material[
36]
Δρ (nΩ·m/wt pct) | 6.11 | 6.68 | 3.32 | 1.01 | 38.00 | 31.43 | 18.48 | 31.92 |
4.1.2 Effect of homogenization heat treatment on electrical resistivity
In the presence of secondary particles, the primary effective parameters on the electrical resistivity are as follows:[
35] (1) the volume fraction of fine and coherent particles in the structure, (2) the particle interspacing, and (3) the concentration of elements in solid solution.
The formation of dispersoids leads to a decrease in the concentration of the corresponding elements in the matrix. If the elements precipitate out during a thermal process such as homogenization or precipitation hardening, the change in the electrical resistivity of the material depends on the size and the interface of the newly formed particles.[
17‐
21] If the new particles are small and coherent, the electrical resistivity of the material increases and
vice versa.[
35] During homogenization of the as-cast 7XXX-series aluminum alloys, the following two major changes in the structure are expected:[
1,
10‐
12,
37] (1) the formation of small particles or dispersoids largely from Zr, Cr, Fe, and Mn and (2) the dissolution of constitutive particles and the formation of new ones, depending on the homogenization temperature and holding time.
Regardless of the interface of the dispersoids formed, it is expected that, if the particle interspacing is greater than the required free-passing distance of the electrons (
i.e., for precipitate interspacing of 100 nm and larger in aluminum alloys), the effect of particles is negligible.[
18,
35] Previous investigations show that the distances between the dispersoids vary depending on the homogenization treatment conditions.[
10‐
12] However, in the present investigation, as shown in Figure
4, the dispersoid interspacing is larger than 150 nm, regardless of the homogenization treatment employed. Thus, there is no increase in the electrical resistivity expected due to the formation of dispersoids. The formation of dispersoids is consistent with the depletion of the corresponding alloying elements from the structure, which may result in a decrease in the electrical resistivity as discussed later.
From Table
II, it is clear that the compositions of the small dispersoids formed during homogenization are primarily enriched with Zr, Cr, Mn, Fe, and some other elements. The fourth type of dispersoid is composed of other elements such as Zn and Mg that affect the electrical resistivity insignificantly. Previous investigations showed that this type of dispersoid is very rarely found in the homogenized structure of AA7020 alloy.[
32] Because the elements constituting the fourth type of dispersoid are less effective on the electrical resistivity compared to Zr, Cr, Mn, and Fe, and also due to the negligible number density of these dispersoids, the following discussion will be focused on the first three types of dispersoids. As discussed earlier, Zr, Cr, Mn, and Fe can affect the electrical resistivity of the alloy significantly. It should be noted that the Mn-containing dispersoids are only formed during homogenization at temperatures higher than 510 °C and holding times larger than 4 hours. The formation of these small particles leads to the depletion of these elements in the matrix, which results in a continuous decrease in the electrical resistivity of the samples, in agreement with Reference
5.
According to Mattiessen’s law, another effective factor on the electrical resistivity is the concentration of elements present in the structure. It is clear in Table
I that the concentrations of Si, Cu, Mg, and Zn, which are likely to dissolve in the aluminum solid solution, are relatively higher than those of Zr, Mn, Cr, and Fe, which are depleted out of the structure. This may indicate that the effect of smaller concentrations of Zr, Mn, Cr, and Fe on the increase in electrical resistivity is larger than the effect of larger amounts of Si, Cu, Mg, and Zn. This is consistent with the data presented in Table
IV illustrating the electrical resistivity of the pure elements.
It is clear in Figure
6 that homogenization at 390 °C leads to an increase in the volume fraction of large particles. At 470 °C, the volume fraction remains unchanged, while at 510 °C and 550 °C, it decreases. At a low-temperature homogenization (390 °C), the dissolution of the large particles does not occur and large
η and
β precipitates form.[
33] Therefore, the electrical resistivity curve in Figure
2 shows a continuous decrease up to 48 hours of homogenization,[
21,
35] due to the depletion of Zr and Cr in the matrix by forming dispersoids and the depletion of Mg, Si, and Zn by the forming of
η and
β precipitates.
During high-temperature homogenization, however, the dissolution of the large particles, including the Al17(Fe3.2Mn0.8)Si2 particles that account for a considerable percentage of Fe and Mn, occurs. Therefore, the presence of Mn-containing dispersoids after homogenization at 510 °C or 550 °C for more than 2 hours is consistent with the dissolution of the Al17(Fe3.2Mn0.8)Si2 particles. It can be concluded that, during homogenization at temperatures lower than 470 °C, the Al17(Fe3.2Mn0.8)Si2 particles are not dissolved in the structure and the concentrations of Fe and Mn in the solid solution are not enough for the formation of Mn-containing dispersoids.
Among all the elements present in the AA7020 aluminum alloy, Mn is the only one that has a mutual effect. In other words, Fe and Mn are present in the Al
17(Fe
3.2Mn
0.8)Si
2 particles and become dissolved during homogenization at high temperatures, resulting in higher Fe and Mn concentrations in the solid solution. They are also present in the third type of dispersoid, which precipitates out during homogenization. As shown in Table
IV, Fe and Mn are the most effective elements that can cause changes in the electrical resistivity. Because the electrical resistivity of the alloy decreases during homogenization at high temperatures, while the Al
17(Fe
3.2Mn
0.8)Si
2 particles are dissolving, it may be concluded that the percentages of Fe and Mn dissolving in the structure from the Al
17(Fe
3.2Mn
0.8)Si
2 particles are equal to or less than the percentages of these elements depleting out from the structure by the formation of the third type of dispersoid.
The formation of the plateau in the electrical resistivity curve (Figure
2) may be due to the balance of the increase in the concentrations of some elements, namely, Si, Mg, and Zn in the matrix, and the depletion of other elements such as Zr and Cr out of the matrix. When the rate of the increase in the electrical resistivity due to the dissolution of constitutive particles and, therefore, the enrichment of the structure becomes equal to the rate of the decrease in the electrical resistivity due to the formation of Zr- and Cr-containing dispersoids, a peak or plateau is observed in the electrical resistivity curve.